A wave equation which gives the displacement along $y$-direction is given by $y = 10^{-4} \sin (60t + x)$,…

A wave equation which gives the displacement along $y$-direction is given by $y = 10^{-4} \sin (60t + x)$, where $x$ and $y$ are in metre and $t$ is time in second. This represents a wave
  1. (a) travelling with a velocity of $300\text{ ms}^{-1}$ in the $-\text{ve } x$-direction
  2. (b) of wavelength $\pi\text{ metre}$
  3. (c) of frequency $\frac{30}{\pi}\text{ Hz}$
  4. (d) of amplitude $10^4\text{ m}$ travelling along the positive $x$-direction

Solution

Angular velocity, $\omega = 2\pi f$ or $60 = 2\pi f$ $\therefore$ Frequency, $f = \frac{30}{\pi}\text{ Hz}$

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